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Learning from spectropolarimetric observations. A. Asensio Ramos Instituto de Astrofísica de Canarias. aasensio.github.io/blog. @ aasensior. github.com/ aasensio. Learning from observations is an ill-posed problem. Follow these four steps. Understand your problem
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Learningfrom spectropolarimetricobservations A. Asensio Ramos Instituto de Astrofísica de Canarias aasensio.github.io/blog @aasensior github.com/aasensio
Followthesefoursteps • Understandyourproblem • Understandthemodelthat ‘generates’ your data • Define a meritfunction • Compute the‘best’ fitbyoptimizingorsamplethismeritfunction Thesolutiontoanymodelfitting has to be probabilistic
Understandyourproblem • Your data has beenobtainedwithaninstrument • Yoursyntheticmodelmightnotexplainwhatyousee • You are surelynotunderstandingyourerrors • Systematics • …
Understandyourgenerativemodel Thisisthemostimportantand complexpart of theinference Example Generativemodel Assumptions • Weassumethat xi are fixed and givenwithzerouncertainty • Uncertainty in themeasurementisGaussianwithzero meanand diagonal covariance
Fromthegenerativemodeltothemeritfunction Likelihood Probabilitythatthemeasured data has been generatedfromthemodel
Why do we do thec2fitting? Thestandardleast-squaresfitting comes fromthe maximization of a Gaussianlikelihood
Somesubtleties • Weights • Do notchangethe position of themaximum • Modifythecurvature at themaximum • Ifnoisestatisticschange, modifythelikelihood
Be aware of theassumptions • Errors are Gaussian • Youknowtheerrors itisdifficulttoestimateuncertaintiesin theerrorsbecauseerrors are already a 2ndorderstatistics • Errors are onlyonthe y axis x locations are givenwithinfiniteprecision • Themodelincludesthetruth
Whatifwe break theassumptions? Any of ourassumptionsmight be broken • Errors are notGaussian • Wedon’tknowtheerrors • Errors are alsoonthex axis • Themodeldoesnotincludethetruth
Withoutliers Wegetbiasedresults
Modeleverything Ifyoumodelthe data points and theoutliers, youautomatically have a generativemodel and a meritfunctiontooptimize pointsfromthe line badpoint
Hazel github.com/aasensio/hazel MIT license
Assumptions+ properties • Multi-term atom • Simplified but realistic radiativetransfer effects • One or two components (along LOS or inside pixel) • Magneto-optical effects • MIT license • MPI using master-slavescheme • Scalesalmostlinearlywith N-1 (testedwithup to 500 CPUs) • Pythonwrapperforsynthesis
3d3D 3p3P 3s3S 2p3P 10830 Å 2s3S
Problemswithinversion • Robustness • Sensitivitytoparameters • Ambiguities
Robustness: 2-step inversion Global convergence DIRECT Refinement Levenberg-Marquardt Step 1 Step 2 Step 3 DIRECT algorithm (Jones et al 93)
Sensitivitytoparameters: cycles Modifyweights and do cycles Cycle 1 Invertthermodynamicalproperties t, Dvth, vDopp, … Stokes I Cycle 2 Invertmagneticfield vector Stokes Q, U, V
Ambiguities: off-limbapproach • Do a firstinversionwithHazel • Saturationregime findtheambiguoussolutions (<8) In thesaturationregime(above~40 G for He I 10830)
Ambiguities: off-limbapproach • Do a firstinversionwithHazel • Saturationregime findtheambiguoussolutions (<8) • Foreachsolution, use Hazelto refine theinversion • NowalmostautomaticallywithHazel
Wheretogofromhere? • Do full Bayesianinversion • Modelcomparison • Inversionswithconstraints Modeleverything, includingsystematics, and integrateoutnuisanceparameters
Bayesianinference PyHazel+PyMultinest
Modelcomparison H0 : simple Gaussian H1 : twoGaussians of equalwidthbutunknownamplitude ratio
Modelcomparison H0 : simple Gaussian H1 : twoGaussians of equalwidthbutunknownamplitude ratio
Modelcomparison ln R=2.22 weak-moderateevidence in favor of model 1
Bayesianhierarchicalmodel Model FV B1,μ1 Model FV b0 B2,μ2 Model FV B3,μ3
Are solar tornadoes and barbsthesame? Coreof the He I line at 1083.0 nm (~0.8’’) • Full Stokes He I line at 1083.0 nm (VTT+TIP II) • Imaging at thecore of the Hα line (VTT - diffractionlimited MOMFBD) • Imaging at thecore of the Ca II K (VTT - diffractionlimited MOMFBD) • Imagingfrom SDO
``Vertical’’ solutions Field inclination
``Horizontal’’ solutions Field inclination
Magneticfieldisrobust • Fields are statisticallybelow 20 G • Someregionsreach 50-60 G • Filamentary vertical structures in magneticfieldstrength
Conclusions • Be aware of yourassumptions • Modeleverythingifpossible • Hazelisfreelyavailable • Ambiguities can be problematic • More worktoputchromosphericinversionsat thelevel of photosphericinversions
Announcement IAC Winter SchoolonBayesianAstrophysics La Laguna, November 3-14, 2014